# Direct Comparison Test Question

• Oct 13th 2009, 11:39 AM
jujab
Direct Comparison Test Question
LIMIT COMPARISON TEST (sorry)

1/[2(square of n) + (cube root of n)] compared with 1/(square of n)

I understand how to do the problem, my question is: how do I know to choose that equation to compare it with when there are two different n's in the denominator (n^1/2) and (n^3/2).
• Oct 13th 2009, 12:54 PM
redsoxfan325
Quote:

Originally Posted by jujab
LIMIT COMPARISON TEST (sorry)

1/[2(square of n) + (cube root of n)] compared with 1/(square of n)

I understand how to do the problem, my question is: how do I know to choose that equation to compare it with when there are two different n's in the denominator (n^1/2) and (n^3/2).

What exactly is the problem?

$\displaystyle \frac{1}{2n^2+\sqrt[3]{n}}$ compared with $\displaystyle \frac{1}{n^2}$

Or did you mean to say "square root of n", in which case it's

$\displaystyle \frac{1}{2\sqrt{n}+\sqrt[3]{n}}$ compared with $\displaystyle \frac{1}{\sqrt{n}}$
• Oct 15th 2009, 01:08 PM
jujab
I meant square root of n, thanks for catching that!